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陆善镇
数学学报,1980,23(4):610~623,-0001,():
-1年11月30日
本文内容为两部分。第一部分中,研究了多重福里哀级数Rmz球形平均(临界指数)的几乎处处收敛性,将古典的关于福里哀级数几乎处处收敛的salem定理在多维情形中的拓广问题给予解决。第二部分中,研究了多重福里哀级数Ralem球形平均(临界指数)的一致收敛,将古典的关于一致收敛的salem-CTeчkиH定理推广到多维情形中去,并且改进了иъ.гOJIyбOB新近的相应结果。这两方面结果的获得均与本文所提出的球形积分这一新概念有着紧密的关系。
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【期刊论文】Weak estimates for commutators of fractional integral operators
陆善镇, DING Yong (丁勇), LU Shanzhen (陆善镇) & ZHANG Pu (张璞)
SCIENCE IN CHINA(Series A), 2002, 45(2):196-213,-0001,():
-1年11月30日
By introducing a kind of maximal operator of the fractional order associated with the mean Luxemburg norm and using the technique of the sharp function, the weak type Llog Lestimates for the commutators of the fractional integral operator and the related maximal operator are established.
fractional integral,, commutator,, sharp function,, Young function,, Luxemburg norm.,
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【期刊论文】Weak estimates for commutators of fractional integral operators
陆善镇, DING Yong (丁勇), LU Shanzhen (陆善镇) & ZHANG Pu (张璞)
SIENCE IN CHINA (Series A), 2001, 44 (7): 877~888,-0001,():
-1年11月30日
By introducing a kind of maximal operator of the fractional order associated with the mean Luxemburg norm and using the technique of the sharp function. the weak type Llog Lestimates for the commutators of the fractional integral operator and the related maximal operator are established.
fractional integral,, commutator,, sharp function,, Young function,, Luxemburg norm.,
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【期刊论文】Two-weight Weak type Norm Inequalities for the Commutators of Fractional Integrals
陆善镇, Zongguang Liu and Shanzhen Lu
Integr. Equ. Oper. Theory 48(2004),397-409,-0001,():
-1年11月30日
In this paper, we obtain a suffcient condition for two-weight weak type norm inequality for the commutators of fractional integral [b, Iα], where b∈BMO and 0<a<n.
Fractional integral,, Commutator., Weight,, Weak type norln inequaliLy,, BMO
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【期刊论文】The local versions of Hp(Rn) spaces at the origin by
陆善镇, SHANZHEN LU and DACHUN YANG
STUDIA MATHEMATICA 116 (2) (1995),-0001,():
-1年11月30日
Let 0<p≤1<q<∞and α=n (1/p-1-q). We introduce some new Hardy spaces HKα,q p (Rn) which are the local versions of Hp(Rn) spaces at the origin. Characterizations of these spaces in terms of atomic and molecular decompositions are established, together with their φ-transform characterizatins in M. Frazier and B. Jawerth's sense. We also prove an interpolation theorem for operators on HKα,qp(Rn) and discuss the HKα,qp (Rn)-boundedness of Calderon-Zygmund operators. similar results can also be obtined for the non-homogeneous Hardy spaces HKα,qp (Rn).
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